Question

Two metal spheres of capacitance, $C_1$ and $C_2$ carry some charges. They are put in contact and then separated. The final charges $Q_1$ and $Q_2$ on them will satisfy:

• A. $\frac{Q_1}{Q_2}<\frac{C_1}{C_2}$
• B. $\frac{Q_1}{Q_2}=\frac{C_1}{C_2}$
• C. $\frac{Q_1}{Q_2}>\frac{C_1}{C_2}$
• D. $\frac{Q_1}{Q_2}=\frac{C_2}{C_1}$

Answer 1

The correct option is B $\frac{Q_1}{Q_2}=\frac{C_1}{C_2}$

Let the charge on two sphere initially are $q_1\&q_2$. Now when these two capacitors (spheres) are kept in contact with each other and separated. Then charges on the two spheres are,

Let $Q_1\&Q_2$ are the final charges on spheres. So, final charge will be conserved.

$Q_1+Q_2=q_1+q_2$

$\frac{Q_1}{Q_2}=\frac{C_1{V}_1}{C_2{V}_2}$

The charge will flow until the potential of both the spheres becomes the same.

$\frac{Q_1}{Q_2}=\frac{C_{1}V}{C_{2}V}$

$\frac{Q_1}{Q_2}=\frac{C_1}{C_2}$